Stability and magnetic properties of Fe double-layers on Ir (111)

We investigate the interplay between the structural reconstruction and the magnetic properties of Fe doublelayers on Ir (111)-substrate using first-principles calculations based on density functional theory and mapping of the total energies on an atomistic spin model. We show that, if a second Fe monolayer is deposited on Fe/Ir (111), the stacking may change from hexagonal close-packed to bcc (110)-like accompanied by a reduction of symmetry from trigonal to centered rectangular. Although the bcc-like surface has a lower coordination, we find that this is the structural ground state. This reconstruction has a major impact on the magnetic structure. We investigate in detail the changes in the magnetic exchange interaction, the magnetocrystalline anisotropy, and the Dzyaloshinskii Moriya interaction depending on the stacking sequence of the Fe double-layer. Based on our findings, we suggest a new technique to engineer Dzyaloshinskii Moriya interactions in multilayer systems employing symmetry considerations. The resulting anisotropic Dzyaloshinskii-Moriya interactions may stabilize higher-order skyrmions or antiskyrmions

Magnetic Interactions in BiFeO3_3: a First-Principles Study

First-principles calculations, in combination with the four-state energy mapping method, are performed to extract the magnetic interaction parameters of multiferroic BiFeO$_3$. Such parameters include the symmetric exchange (SE) couplings and the Dzyaloshinskii-Moriya (DM) interactions up to second nearest neighbors, as well as the single ion anisotropy (SIA). All magnetic parameters are obtained not only for the $R3c$ structural ground state, but also for the $R3m$ and $R\bar{3}c$ phases in order to determine the effects of ferroelectricity and antiferrodistortion distortions, respectively, on these magnetic parameters. In particular, two different second-nearest neighbor couplings are identified and their origins are discussed in details. Moreover, Monte-Carlo (MC) simulations using a magnetic Hamiltonian incorporating these first-principles-derived interaction parameters are further performed. They result (i) not only in the accurate prediction of the spin-canted G-type antiferromagnetic structure and of the known magnetic cycloid propagating along a $$ direction, as well as their unusual characteristics (such as a weak magnetization and spin-density-waves, respectively); (ii) but also in the finding of another cycloidal state of low-energy and that awaits to be experimentally confirmed. Turning on and off the different magnetic interaction parameters in the MC simulations also reveal the precise role of each of them on magnetism

Dzyaloshinskii-Moryia interaction at an antiferromagnetic interface: first-principles study of FeIr bilayers on Rh(001)

We study the magnetic interactions in atomic layers of Fe and 5d transition-metals such as Os, Ir, and Pt on the (001) surface of Rh using first-principles calculations based on density functional theory. For both stackings of the 5d-Fe bilayer on Rh(001) we observe a transition from an antiferromagnetic to a ferromagnetic nearest-neighbor exchange interaction upon 5d band filling. In the sandwich structure 5d/Fe/Rh(001) the nearest neighbor exchange is significantly reduced. For FeIr bilayers on Rh(001) we consider spin spiral states in order to determine exchange constants beyond nearest neighbors. By including spin-orbit coupling we obtain the Dzyaloshinskii-Moriya interaction (DMI). The magnetic interactions in Fe/Ir/Rh(001) are similar to those of Fe/Ir(001) for which an atomic scale spin lattice has been predicted. However, small deviations between both systems remain due to the different lattice constants and the Rh vs. Ir surface layers. This leads to slightly different exchange constants and DMI and the easy magnetization direction switches from out-of-plane for Fe/Ir(001) to in-plane for Fe/Ir/Rh(001). Therefore a fine tuning of magnetic interactions is possible by using single 5d transition-metal layers which may allow to tailor antiferromagnetic skyrmions in this type of ultrathin films. In the sandwich structure Ir/Fe/Rh(001) we find a strong exchange frustration due to strong hybridization of the Fe layer with both Ir and Rh which drastically reduces the nearest-neighbor exchange. The energy contribution from the DMI becomes extremely large and DMI beyond nearest neighbors cannot be neglected. We attribute the large DMI to the low coordination of the Ir layer at the surface. We demonstrate that higher- order exchange interactions are significant in both systems which may be crucial for the magnetic ground state

Mechanism for the {\alpha} -> {\epsilon} phase transition in iron

The mechanism of the {\alpha}-{\epsilon} transition in iron is reconsidered. A path in the Burgers description of the bcc/hcp transition different from those previously considered is proposed. It relies on the assumption that shear and shuffle are decoupled and requires some peculiar magnetic order, different from that of {\alpha} and {\epsilon} phases as found in Density-Functional Theory. Finally, we put forward an original mechanism for this transition, based on successive shuffle motion of layers, which is akin to a nucleation-propagation process rather than to some uniform motion.Comment: 6 pages, 5 figure

Revealing the correlation between real-space structure and chiral magnetic order at the atomic scale

We image simultaneously the geometric, electronic and magnetic structure of a buckled iron bilayer film that exhibits chiral magnetic order. We achieve this by combining spin-polarized scanning tunneling microscopy and magnetic exchange force microscopy (SPEX), to independently characterize the geometric as well as the electronic and magnetic structure of non-flat surfaces. This new SPEX imaging technique reveals the geometric height corrugation of the reconstruction lines resulting from strong strain relaxation in the bilayer, enabling the decomposition of the real-space from the eletronic structure at the atomic level, and the correlation with the resultant spin spiral ground state. By additionally utilizing adatom manipulation, we reveal the chiral magnetic ground state of portions of the unit cell that were not previously imaged with SP-STM alone. Using density functional theory (DFT), we investigate the structural and electronic properties of the reconstructed bilayer and identify the favorable stoichiometry regime in agreement with our experimental result

B-T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo

We use an atomistic spin model derived from density functional theory calculations for the ultra-thin film Pd/Fe/Ir(111) to show that temperature induces coexisting non-zero skyrmion and antiskyrmion densities. We apply the parallel tempering Monte Carlo method in order to reliably compute thermodynamical quantities and the B-T phase diagram in the presence of frustrated exchange interactions. We evaluate the critical temperatures using the topological susceptibility. We show that the critical temperatures depend on the magnetic field in contrast to previous work. In total, we identify five phases: spin spiral, skyrmion lattice, ferromagnetic phase, intermediate region with finite topological charge and paramagnetic phase. To explore the effect of frustrated exchange interactions, we calculate the B-T phase diagram, when only effective exchange parameters are taken into account.Comment: 8 figure

Engineering magnetic domain wall energies in multiferroic BiFeO3_3 via epitaxial strain

Epitaxial strain has emerged as a powerful tool to tune magnetic and ferroelectric properties in functional materials such as in multiferroic perovskite oxides. Here, we use first-principles calculations to explore the evolution of magnetic interactions in the antiferromagnetic multiferroic BiFeO$_3$ (BFO), one of the most promising multiferroics for future technology. The epitaxial strain in BFO(001) oriented film is varied between $\varepsilon_{xx,yy}$ $\in$ $[-2\%, +2\%]$. We find that both strengths of the exchange interaction and Dzyaloshinskii-Moriya interaction (DMI) decrease linearly from compressive to tensile strain whereas the uniaxial magnetocrystalline anisotropy follows a parabolic behavior which lifts the energy degeneracy of the (111) easy plane of bulk BFO. From the trends of the magnetic interactions we can explain the destruction of cycloidal order in compressive strain as observed in experiments due to the increasing anisotropy energy. For tensile strain, we predict that the ground state remains unchanged as a function of strain. By using the domain wall (DW) energy, we envision the region where isolated chiral magnetic texture might occur as function of strain i.e. where the DW and the spin spiral energy are equal. This transition between $-1.5\%$ and $-0.5\%$ of strain should allow topologically stable magnetic states such as antiferromagnetic skyrmions and merons to occur. Hence, our work should trigger experimental and theoretical investigations in this range of strain

Trochoidal motion and pair generation in skyrmion and antiskyrmion dynamics under spin-orbit torques

Skyrmions and antiskyrmions in magnetic ultrathin films are characterised by a topological charge describing how the spins wind around their core. This topology governs their response to forces in the rigid core limit. However, when internal core excitations are relevant, the dynamics become far richer. We show that current-induced spin-orbit torques can lead to phenomena such as trochoidal motion and skyrmion-antiskyrmion pair generation that only occurs for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii-Moriya interaction. Such dynamics are induced by core deformations, leading to a time-dependent helicity that governs the motion of the skyrmion and antiskyrmion core. We compute the dynamical phase diagram through a combination of atomistic spin simulations, reduced-variable modelling, and machine learning algorithms. It predicts how spin-orbit torques can control the type of motion and the possibility to generate skyrmion lattices by antiskyrmion seeding

Spin-current driven Dzyaloshinskii-Moriya interaction in the multiferroic BiFeO3 from first-principles

The electrical control of magnons opens up new ways to transport and process information for logic devices. In magnetoelectrical multiferroics, the Dzyaloshinskii-Moriya (DM) interaction directly allow for such a control and, hence, is of major importance. We determine the origin and the strength of the (converse) spin current DM interaction in the R3c bulk phase of the multiferroic BiFeO3 based on density functional theory. Our data supports only the existence of one DM interaction contribution originating from the spin current model. By exploring then magnon dispersion in the full Brillouin Zone, we show that the exchange is isotropic, but the DM interaction and anisotropy prefer any propagation and any magnetization direction within the full (111) plane. Our work emphasizes the significance of the asymmetric potential induced by the spin current over the structural asymmetry induced by the anionic octahedron in multiferroics such as BiFeO3

Comparison of first-principles methods to extract magnetic parameters in ultra-thin films: Co/Pt(111)

We compare three distinct computational approaches based on first-principles calculations within density functional theory to explore the magnetic exchange and the Dzyaloshinskii-Moriya interactions (DMI) of a Co monolayer on Pt(111), namely (i) the method of infinitesimal rotations of magnetic moments based on the Korringa-Kohn-Rostoker (KKR) Green function method, (ii) the generalized Bloch theorem applied to spiraling magnetic structures and (iii) supercell calculations with non-collinear magnetic moments, the latter two being based on the full-potential linearized augmented plane wave (FLAPW) method. In particular, we show that the magnetic interaction parameters entering micromagnetic models describing the long-wavelength deviations from the ferromagnetic state might be different from those calculated for fast rotating magnetic structures, as they are obtained by using (necessarily rather small) supercell or large spin-spiral wave-vectors. In the micromagnetic limit, which we motivate to use by an analysis of the Fourier components of the domain-wall profile, we obtain consistent results for the spin stiffness and DMI spiralization using methods (i) and (ii). The calculated spin stiffness and Curie temperature determined by subsequent Monte Carlo simulations are considerably higher than estimated from the bulk properties of Co, a consequence of a significantly increased nearest-neighbor exchange interaction in the Co-monolayer (+50%). The calculated results are carefully compared with the literature